Rational vs Irrational

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

An irrational number is a number that cannot be expressed as a simple fraction; it cannot be written as a ratio of two integers.

Rational; The sum of two rational numbers is always rational.

Irrational; The sum of a rational number and an irrational number is always irrational.

Rational; The product of two rational numbers is always rational.

Irrational; The product of a nonzero rational number and an irrational number is always irrational.

A perfect square is a number that can be expressed as the square of an integer.

Rational; The square root of a perfect square is always a rational number.

Rational; It can be expressed as a fraction of two integers.

Irrational; The square root of 2 is irrational.